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This paper presents recent Lower Hybrid Current Drive (LHCD) progress in SWIP, including the experiments on HL-2A and system development on HL-2M. The 3.7GHz LHCD system was built on HL-2A, where the first Lower Hybrid Wave (LHW) coupling to H-mode plasma experiment via Passive-Active Multijunction (PAM) launcher was carried out. The coupled power has been increased much from 470kW to 1400kW since 2014. The LHW power became more and more important in the H-mode discharges on HL-2A in the past 4 years. In 2018, 1.1s ELMy H-mode was achieved with the help of Neutral Beam Injection (NBI) and LHW injection. However, The LHCD experiments showed distinct characteristic on HL-2A, i.e. no full non-inductive current drive (loop voltage never dropped below 0.3V) and counter-current drive effect found in the situation of co-current drive spectrum. Full non-inductive current drive was finally obtained after the spectrum turned opposite. Besides those achievements, the abnormal LHCD phenomenon discussion, full non-inductive current drive experiments, co-current and counter-current comparison, LHW deposition and mechanism of LHCD ELM mitigation are described. At the same time, a 4MW LHCD system is planned to be constructed on HL-2M. A 2MW LHCD system has been developed for HL-2M tokamak until now. Four TH2103C1 klystrons, transmission lines and a 4MW FAM antenna are included in this system. The other part will be built soon.

The exact analytical solution of the one-dimensional diffusion equation in a cylinder has been found, for a medium characterized by a diffusion coefficient with step-like and/or monomial variations, in addition to a constant damping term. This type of equation has important applications in the field of magnetically confined plasmas, in the presence of a transport barrier. A sharp variation of the heat diffusivity can also result from the microturbulence that develops whenever the temperature gradient exceeds a critical value. This analytical solution can be used to model the evolution, in space and time, of the electron temperature of a plasma heated up by an external source, the step in the heat diffusion coefficient being related to the space location of the critical temperature gradient. The general properties of the solution and its application to the analysis of perturbative electron heating experiments are discussed.

In neutral beam injection and ion cyclotron resonance frequency (NBI+ICRF) heated high-temperature Joint European Torus (JET) plasmas, electron cyclotron emission (ECE) spectra measured by the Michelson interferometer are inconsistent with the electron bulk distribution being Maxwellian. This conclusion follows from new, accurate modeling of the ECE spectra over the full measured frequency range, covering the first four harmonics of the cyclotron frequency. A model distribution function obtained by fitting a measured ECE spectrum reveals a distortion of the Maxwellian that is sharply localized at ∼1.5×thermal momentum. A consequence deduced from this distribution is that the electron temperature measured by JET’s Thomson scattering diagnostic, which weighs the bulk electrons differently, should be lower than the ECE one in the spatial region where this distortion exists. This prediction appears to be confirmed by temperature profile comparisons showing that core Thomson scattering electron temperatures on JET are up to 20% lower than ECE values for plasmas with strong NBI+ICRF heating. The possibility of addressing experimentally the question of whether the plasma has a Maxwellian bulk is also discussed. This goal can be accomplished by observing the emission at different angles with respect to the magnetic field (oblique ECE). Simulations of oblique ECE spectra using the model distribution function obtained previously show an angular variation of the emission that is characteristic of the distorted bulk.

Edge localized mode (ELM) mitigation with lower hybrid current drive (LHCD) has been observed in the HL-2A tokamak. This mitigation effect is very sensitive to the parameters as the plasma density and the LHCD absorbed power, i.e., more easily to be observed for high density and large LHCD absorbed power. The divertor peak heat load released by ELM has been significantly reduced during the mitigation phase. The pedestal density gradient is slightly reduced during ELM mitigation, and the plasma rotation velocity and ion temperature are significantly reduced by LHCD. It has been found that the ELM mitigation is not synchronized with the LHCD, while it is synchronized with the increase of the pedestal turbulence, showing that the enhancement of the transport due to the pedestal turbulence can be the direct cause of the ELM mitigation.

A numerical model for predictive simulations of radiofrequency current drive in magnetically confined plasmas is developed. It includes the minimum requirements for a self-consistent description of such regimes, i.e., a three-dimensional kinetic equation for the electron distribution function, one-dimensional heat and current transport equations, and resonant coupling between velocity space and configuration space dynamics, through suitable wave propagation equations. The model finds its full application in predictive studies of complex current profile control scenarios in tokamaks, aiming at the establishment of internal transport barriers by the simultaneous use of various radiofrequency current drive methods. The basic properties of this nonlinear numerical system are investigated and illustrated by simulations applied to reversed magnetic shear regimes obtained by Lower Hybrid and Electron Cyclotron current drive for parameters typical of the Tore Supra tokamak [Equipe Tore Supra, in Proceedings of th...

Numerical modeling of the stabilization of neoclassical tearing modes by localized radio frequency (rf) current drive is presented. The bootstrap current is self-consistently calculated from the pressure evolution equation, the rf current source is obtained from the ray-tracing code and the Fokker–Planck code, and the change of the driven current profile due to the change of the magnetic island width has also been taken into account by modeling the two-dimensional transport of the fast electrons induced by the rf wave. It is found that both parallel and the perpendicular transport of the fast electrons play important roles in the stabilization, and modulated and nonmodulated rf current drive have approximately the same stabilizing effect. The neoclassical tearing modes is shown to be stabilized by a continuous rf current drive. The simulation results essentially agree with experimental observations.

The evolution of the wave polarization during the propagation of electron cyclotron waves in hot plasmas is investigated. The coupled mode equations are solved in slab geometry, including the relativistic corrections to the dielectric tensor. This formalism is applied to purely ordinary or extraordinary modes, propagating obliquely with respect to the magnetic field in tokamak plasmas, in order to determine the rate of change of the mode purity due to finite temperature effects. It is found that such an alteration of the mode purity can be one to three orders of magnitude larger than in a cold plasma. However, the overall effect remains tolerable for most applications and typical parameters of magnetically confined plasmas.

Lower hybrid (LH) current drive experiments on the Princeton Beta Experiment-Modified (PBX-M) [Phys. Fluids B 2, 1271 (1990)] have shown that the current profile can be changed by varying the phase velocity of the waves. The radial profile of the current carrying electrons was deduced from two-dimensional hard x-ray tomography. For a certain range of phase velocities, there is a correlation between the peak of the fast electron profile and the launched wave spectrum, despite the presence of a wide spectral gap between the phase velocity and the thermal electron energy distribution. A new model is proposed to explain how first-pass wave damping is possible in such plasmas. The rf power can form a tail of energetic electrons, and subsequently waves with moderate phase velocity can damp on them. For waves with very fast phase velocity, there must be an upshift of the n∥ spectrum for any damping to occur. These hypotheses are supported by ray tracing results which are coupled to relativistic Fokker–Planck cal...

Emission of cyclotron radiation at arbitrary wave frequency for diagnostic purposes is discussed. It is shown that the radiation spectrum at arbitrary frequencies is more informative than the first few harmonics and it is suited for diagnosis of superthermal electrons without any ‘‘ad hoc’’ value of the wall reflection coefficient. Thermal radiation from the Tokamak Fusion Test Reactor (TFTR) [Fusion Technol. 21, 1324 (1992)] is investigated and it is shown that the bulk and the tail of the electron momentum distribution during strong neutral beam injection is a Maxwellian with a single temperature in all ranges of electron energies.

Emission of synchrotron radiation for electron temperature diagnostics in dense and hot tokamak plasmas is discussed. This novel diagnostic scheme is motivated by the need to overcome several limitations of the familiar first and second harmonic method, caused by cutoff, refraction, and harmonic overlap. Emission at high harmonics is not restricted by density and temperature upper limits, and the method is then particularly appropriate for reactor relevant regimes. This method yields global information on the electron temperature profile, since the source of high harmonic emission is poorly localized in space. Synchrotron radiation is emitted by electrons over a wide spectrum of energies, ranging from thermal to superthermal values, and is therefore also useful to investigate deviations of the electron velocity distribution from the Maxwellian. In contrast, the source of the optically thick low harmonic radiation is highly localized in the ordinary space near the resonance points, which implies that the e...

Recent hardware improvements on the hard x‐ray camera of the Princeton Beta Experiment‐Modified (PBX‐M) expand the capabilities for observing bremsstrahlung radiation from fast electrons during lower hybrid current drive (LHCD) experiments, thereby allowing accurate fast electron transport studies. Developed methods to directly invert two‐dimensional x‐ray images reveal radial profiles of the emitted intensity and isotropy. Such profiles extracted from lower hybrid (LH) modulation experiments permit computation of the lower hybrid power absorption profile. Results from application to the LH phase scans demonstrate the ability to control the peak location of the driven current. Incorporating these results into simulations using both a three‐dimensional Fokker–Planck code and a simple modulation model provides lower and upper bound estimates for the hot electron diffusion coefficient D*.

The Hamiltonian formalism is used to address the problem of the direct resonant interaction between the fast magnetosonic wave and the electrons in a tokamak plasma. The intrinsic stochasticity of the electron trajectories in phase space is first derived. Together with extrinsic decorrelation processes, it assesses the validity of the quasilinear approximation for the kinetic studies of fast wave current drive (FWCD). A full‐wave solution of the Maxwell–Vlasov set of equations provides the exact pattern of the wave fields in the tokamak geometry, consistent with a realistic antenna spectrum. The local quasilinear diffusion tensor is then derived from the wave fields and the driven current density profile, the power deposition profile and the current drive efficiency are computed, including possible nonlinear effects in the kinetic equation. Several applications of FWCD on existing and future machines are given, and the combination of FWCD with other noninductive current drive methods is investigated. Fina...

Synchrotron radiation in a tokamak with inhomogeneous plasma parameters is investigated to determine the role of the temperature profile on the global loss. Using reactor relevant parameters, it is shown that synchrotron radiation is profile dependent, namely, at constant thermal energy, the emitted radiation increases with the peak temperature. An approximated analytical formula for the global loss is found.

A method for measuring the radial profile of the lower‐hybrid‐driven current in a low‐density tokamak plasma using electron‐cyclotron wave attenuation is discussed. This diagnostic scheme is reminiscent of the transmission interferometry approach, commonly used in tokamaks to measure the plasma density, but now the wave amplitude instead of the phase is measured. Wave attenuation of the ordinary mode at ωp ≪ ω < ωc along vertical chords is measured; at these frequencies, the waves are absorbed by the superthermal tail sustained by lower‐hybrid waves and the local wave absorption coefficient is proportional to the noninductive current density. The radial profile of this current is obtained from Abel inversion. An application to the Tore Supra tokamak is presented.

The radiation source wavelength useful for a Collective Thomson Scattering (CTS) on ITER is analyzed in this paper, and the related scattering geometry, signal to noise ratio and technology needed for the measurement of the alpha particles are specified. The ITER plasma parameters taken for reference1 in the calculations are: ne= 1.2 1020m-3, Te = 22keV , Ti = 20KeV, n∝/ne = 0.0017, BT=5.7T, R =8.1m,a=3.0m,k=1.55.The plasma, machine and alpha parameters are quite different from those included in the first proposal2 for a Collective Scattering System, where a FEL(Free Electron Laser) source at 1.5THz(λ=200µm) was proposed.In the present work three sources are considered with wavelength λ=l0.6µm(CO2 laser P(20)line), 200µm(FEL),4.61mm(65GHz gyrotron). For the evaluation of source figures the calculation of ECE background radiation level is needed, after some geometry constraints are discussed,and then the evaluation of scattered power and signal to noise ratio is performed, adding observations on the technology needed.

A system for vertically observing the second‐harmonic electron‐cyclotron emissions from the TEXT‐U tokamak in conjunction with fundamental electron‐cyclotron heating is described. Using external collection optics and heterodyne receivers, measurements of the distribution function can be performed over two‐thirds of the plasma radius and on transport time scales. Observations are typically of electrons with energy E

The development of operating scenarios is one of the key issues in the research for ITER which aims to achieve a fusion gain (Q) of ∼10, while producing 500 MW of fusion power for ≥300 s. The ITER Research plan proposes a success oriented schedule starting in hydrogen and helium, to be followed by a nuclear operation phase with a rapid development towards Q ∼ 10 in deuterium/tritium. The Integrated Operation Scenarios Topical Group of the International Tokamak Physics Activity initiates joint activities among worldwide institutions and experiments to prepare ITER operation. Plasma formation studies report robust plasma breakdown in devices with metal walls over a wide range of conditions, while other experiments use an inclined EC launch angle at plasma formation to mimic the conditions in ITER. Simulations of the plasma burn-through predict that at least 4 MW of Electron Cyclotron heating (EC) assist would be required in ITER. For H-modes at q95 ∼ 3, many experiments have demonstrated operation with scaled parameters for the ITER baseline scenario at ne/nGW ∼ 0.85. Most experiments, however, obtain stable discharges at H98(y,2) ∼ 1.0 only for βN = 2.0–2.2. For the rampup in ITER, early X-point formation is recommended, allowing auxiliary heating to reduce the flux consumption. A range of plasma inductance (li(3)) can be obtained from 0.65 to 1.0, with the lowest values obtained in H-mode operation. For the rampdown, the plasma should stay diverted maintaining H-mode together with a reduction of the elongation from 1.85 to 1.4. Simulations show that the proposed rampup and rampdown schemes developed since 2007 are compatible with the present ITER design for the poloidal field coils. At 13–15 MA and densities down to ne/nGW ∼ 0.5, long pulse operation (>1000 s) in ITER is possible at Q ∼ 5, useful to provide neutron fluence for Test Blanket Module assessments. ITER scenario preparation in hydrogen and helium requires high input power (>50 MW). H-mode operation in helium may be possible at input powers above 35 MW at a toroidal field of 2.65 T, for studying H-modes and ELM mitigation. In hydrogen, H-mode operation is expected to be marginal, even at 2.65 T with 60 MW of input power. Simulation code benchmark studies using hybrid and steady state scenario parameters have proved to be a very challenging and lengthy task of testing suites of codes, consisting of tens of sophisticated modules. Nevertheless, the general basis of the modelling appears sound, with substantial consistency among codes developed by different groups. For a hybrid scenario at 12 MA, the code simulations give a range for Q = 6.5–8.3, using 30 MW neutral beam injection and 20 MW ICRH. For non-inductive operation at 7–9 MA, the simulation results show more variation. At high edge pedestal pressure (Tped ∼ 7 keV), the codes predict Q = 3.3–3.8 using 33 MW NB, 20 MW EC, and 20 MW ion cyclotron to demonstrate the feasibility of steady-state operation with the day-1 heating systems in ITER. Simulations using a lower edge pedestal temperature (∼3 keV) but improved core confinement obtain Q = 5–6.5, when ECCD is concentrated at mid-radius and ∼20 MW off-axis current drive (ECCD or LHCD) is added. Several issues remain to be studied, including plasmas with dominant electron heating, mitigation of transient heat loads integrated in scenario demonstrations and (burn) control simulations in ITER scenarios.

The kinetic theory of rf current drive in tokamak plasmas in the presence of magnetic turbulence is investigated. The main effect of the turbulence is to cause radial diffusion of the superthermal electrons. For typical parameters of large machines, the diffusion time can be of the same order of the slowing‐down time of the current carriers. In these conditions, a significant regime is identified in which the total driven current is enhanced by the effect of the radial diffusion. This is demonstrated analytically in the weak turbulence limit, and numerically confirmed in the general case, by means of a fully three‐dimensional Fokker–Planck code, for both parallel and perpendicular velocity‐space diffusion.

The regime of nonlinear temperature oscillations (O-regime), characteristic of noninductive discharges on Tore Supra [Equipe Tore Supra, Proceedings of the 12th International Conference on Plasma Physics and Controlled Nuclear Fusion Research, Nice, France, 1988 (International Atomic Energy Agency, Vienna, 1989), Vol. 1, p. 9], is investigated in its triggering and suppressing mechanism. This regime can be described by two nonlinearly coupled equations for the current density j(r) and the electron temperature Te(r) where the equation coefficients are functions of j and Te themselves. Both the integrated modeling code CRONOS [V. Basiuk et al., Nucl. Fusion 43, 822 (2003)] and a two-patch predator-prey system with diffusion and noise have been used and results have been compared to the experimental observations of the O-regime. A database of discharges is analyzed which features monotonic, flat, and reversed safety factor (q) profiles in order to characterize the action of external actuators on the regime d...

A 32-channel, 1GHz spaced heterodyne radiometer is used on the Tore Supra tokamak to measure electron cyclotron emission (ECE) in the frequency range 78–110GHz for the ordinary mode (O:E‖B,k⊥B) and 94–126GHz for the extraordinary mode (X:E⊥B,k⊥B). The radial resolution is essentially limited by ECE relativistic effects, depending on electron temperature and density, and not by the channels’ frequency spacing. The time resolution depends on the acquisition scheme: the system allows for both 1ms and 10μs acquisition. For example, this leads to precise electron temperature mapping during MHD activity. First experimental results obtained with this upgraded 32-channel radiometer are presented.

The analytical solution of the one-dimensional diffusion-convection equation in a cylinder has been found, for various functional forms of the diffusion coefficient, convection velocity and with an additional damping term. This is a significant generalization of a previous work [A. Clemencon, C. Guivarch, S. P. Eury, X. L. Zou, and G. Giruzzi, Phys. Plasmas 11, 4998 (2004)] on the diffusion equation, including now a convection term that can be constant, monomially increasing in the space coordinate, or have step-like variations. This type of equation has important applications in the field of magnetically confined plasmas, in which convection effects are experimentally observed in both particle and energy transports. Sharp variations of heat diffusivity, convection velocity, and damping term can result from the microturbulence which develops whenever the temperature gradient exceeds a critical value. A general scheme is developed to connect solutions in domains with different functional forms of the coefficients. The properties of the solutions are illustrated and discussed.

The conclusion reached in ref. 1 that the 3‐D Fokker‐Planck code verses the 2‐D bounce‐averaged code does not yield the correct current density is prove to be wrong. It is aruged that the results for the 3‐D code are very close to those of the 2‐D code that employs a bounce‐average procedure.(AIP)

The combined effects of the dc electric field and electron‐cyclotron wave absorption in tokamak plasmas are investigated. The case of the ordinary mode for nearly normal propagation from the low magnetic field side is studied by a two‐dimensional Fokker–Planck code. It is found that the small fraction of the wave energy that goes into the superthermal electrons enhances the effect of the continuous pushing of the tokamak electric field.

The ordinary mode damping near the electron‐cyclotron frequency is investigated using the relativistic dispersion relation. It is shown that the Doppler splitting of the absorption spectrum claimed by Arunasalam et al. [Phys. Rev. A 36, 3909 (1987); 37, 2063 (1988)] is an erroneous result obtained from an oversimplified dispersion relation and assuming an infinite speed of light in the resonance condition.

The general properties of electron cyclotron radiation emitted by the current‐carrying superthermal tail in tokamak plasmas are investigated. Two situations are considered, namely, the case of an extended tail as it occurs in present‐day experiments and that in which the velocity range of the tail is much less than its mean speed. For the former case, we show that most of the emitted radiation obeys Kirchhoff’s law. In the latter case, which is suited for reactor‐like parameters, a simple relation is obtained between the tail momentum distribution and the radiation temperature.

Wave absorption near the electron cyclotron gyrofrequency by the current‐carrying energetic tail in tokamak plasmas is investigated. It is shown that by the proper choice of the angle of propagation, strong wave damping occurs for wave frequencies much less than the central electron cyclotron frequency and that the extraordinary mode can be launched from the low magnetic field side of the torus. It is also found that wave absorption is weakly dependent on the perpendicular temperature of the resonant particles.

The perpendicular propagation of the extraordinary wave near the second electron cyclotron harmonic is analyzed by means of a numerical code embodying a full wave relativistic scheme. Discussion of the results in comparison with the standard WKB ones is performed in view of absorption and emission applications. It is found that in the density regime called the ’’overcritical case’’ the effective optical depth scales, as an effect of the increased interaction of the extraordinary wave with a quasielectrostatic wave, differently from the WKB estimate. An explicit evaluation of reflection and transmission coefficients is given.

Emission and absorption of electron cyclotron radiation in a tokamak plasma in the presence of a fast‐electron tail is investigated. Specifically, the case in which the perpendicular temperature of the very end of the tail has a sharp rise is discussed. This situation occurs during rf current drive, and wave emission and transmission measurements may yield accurate information on the tail formation. The theory is developed for propagation in a homogeneous magnetic field and applies to the vertical direction of the tokamak. The quasilinear theory of wave absorption is also investigated. This study is motivated by the possibility of remote control of temperature anisotropy instability by electron cyclotron heating. The case of the extraordinary mode propagating from the low‐magnetic‐field side of the torus in the equatorial plane is numerically discussed.

The theory of current drive by the combined effects of lower‐hybrid and electron‐cyclotron wave absorption is investigated. The case of a spatially homogeneous lower‐hybrid diffusion coefficient and the electron ordinary mode propagating nearly normal to the magnetic field is considered. The effect of selective electron‐cyclotron wave absorption for optimizing lower‐hybrid current drive is discussed for two situations, namely, the wave frequency close to or much less than the electron‐cyclotron gyrofrequency, which corresponds to particle heating for moderate velocities and mildly relativistic energies, respectively. In the former case, by using the numerical solution of the Fokker–Planck equation it is shown that electron heating is suited for controlling the density of the current‐carrying tail. The latter case is investigated for moderate wave powers and is shown to be most appropriate for optimizing the ratio J/P.

The power dependence of the wave damping in a tokamak plasma for arbitrary direction of propagation, mode of polarization, and wave frequency is investigated. Using a 2‐D Fokker–Planck code, it is shown that the wave damping increases or decreases with the rf power depending on the velocity range of the absorbing electrons.

Electron‐cyclotron resonance absorption for oblique propagation at frequency significantly below the central electron gyrofrequency is considered. It is shown that the extraordinary mode for external launching is suited for additional heating in a tokamak reactor. The properties of wave damping at downshifted frequencies are discussed and are found to differ from those at f≊fc. Using the ray‐tracing code, the wave damping of the e mode is investigated at high densities for which strong refraction of the wave beam occurs.